Two-arc transitive graphs admitting a two-dimensional projective linear group

Let Gamma be a finite connected regular graph. A 2-arc of Gamma is a triple (alpha(0), alpha(1), alpha(2)) of vertices such that alpha(0)not equal alpha(2) and alpha(1) is adjacent to alpha(0) and alpha(2). A graph Gamma is said to be (G, 2)-arc transitive if G less than or equal to Aut(Gamma) and G is transitive on the 2-arcs of Gamma. This paper gives a classification of connected regular graphs Gamma which are (G,2)-arc transitive, where PSL(2,q) less than or equal to G less than or equal to P Gamma L(2,q).